Vis-Viva Equation Solver

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Earth & Space (astronomy, orbital mechanics, meteorology, geology, geodesy, oceanography)

Tranche

tranche-4

Evidence ID

t4-185

Ledger rows

1

No ledger note is attached.

Review findings

NEEDS_REVIEW because the formula is valid, but the output requires an unstated square-root operation and the units, central body, GM-table selection, and two-body assumptions are not specified. The honest_label field is empty.

Formula and scope findings

• The vis-viva equation is standard for two-body orbital motion, but the displayed formula computes v², while the stated output is velocity; the implementation must return the positive root v = sqrt(GM(2/r - 1/a)).
• The formula assumes an ideal two-body model with negligible third-body, drag, and non-spherical-gravity effects.

Unit assumptions

• GM must be the gravitational parameter of the central body, not G alone.
• GM, r, and a must use mutually consistent units; GM in km³/s² with distances in km produces velocity in km/s, while GM in m³/s² with distances in m produces velocity in m/s.
• r is assumed to be the center-to-object orbital radius, not altitude above the body's surface.
• For an elliptical orbit, a > 0, r > 0, and the radicand must be nonnegative; a physically valid orbit also requires the supplied r to lie within that orbit's periapsis and apoapsis radii.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The specification provides no explicit input validation for r=0 or for a negative square-root radicand. Such inputs produce undefined results and must be rejected. The output also lacks a stated sign convention, so it cannot distinguish velocity direction from speed magnitude.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "GM_km3_s2": 398600,
    "r_km": 7000,
    "a_km": 7000
  },
  "expected_outputs": {
    "velocity_km_s": 7.5460491
  },
  "working": "v² = 398600 × (2/7000 - 1/7000) = 398600 × (1/7000) = 56.9428571 km²/s². v = sqrt(56.9428571) = 7.5460491 km/s."
}

Related workflows

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json